Plot Utilities

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Plot Utilities

vx vy char size clr plotG n vx length : plot vx 1 el vy 1 el char size clr augment : i 2 n range plot plot vx i el vy i el char size clr augment stack : for plot 41 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

L-M <= courtesy ... Carlos 2018_09_20

HEADER ITER S:x.1 S:x.2 S:x.3 S:x.4 Res1 μ dnor 18 mat :

t 1012 -^0.51 0.82 1.02 1.23 1.43 1.85 2.05 2.36 4.52 9.22 111 mat :

y 0.78 0.8 0.92 1.14 1.26 1.28 1.22 1.16 1.12 1.08 1.08 111 mat :

model function to fit wrt data set x β f β 2 el β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ / + β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ (2^/ x β 3 el / (β 4 el^* β 4 el * - (:

X x 1 el x 2 el x 3 el x 4 el 41 mat :

n X length : m t length : 21 line

3 appVersion 0.98.6179 ≡ Timing_LM ~ 1.5 min ≡ ConjugateGradient 7 s ≡ 31 line

t0 1 time :

L-M Components

t X ia X 2 el X 1 el X 2 el - 1 t X 3 el / (X 4 el^+ / + X 1 el X 2 el - 1 t X 3 el / (X 4 el^+ (2^/ t X 3 el / (X 4 el^* X 4 el * - :

i 1 m range ΦΦ i el t i el X ia y i el - : for X Φ ΦΦ : 21 line

i 1 m range j 1 n range X j el X j el h + : jjh1 t i el X ia y i el - : X j el X j el 2 h * - : jjh2 t i el X ia y i el - : jjh0 i j el jjh1 jjh2 - 2 h * / : X j el X j el h + : 61 line for 11 line for

X derfhφ jjh0 :

initialise the solver x 111414 mat transpose :

Eps 11012 -^* :

L-M algorithm

h Eps sqrt abs : μ 0.01 : μ1 104.5069 : 31 sys

tol Eps sqrt x normi * :

cont 0 : dnor 1 : update 1 : 31 line dnor tol > update 1 ≡ f x Φ : J x derfhφ : jtj J transpose J * : res f norme (2^: 41 line if 11 line a jtj μ n identity * + : s1 a 1 -^J transpose f * (* : b1 x s1 - (: f1 b1 Φ : res1 f1 norme (2^μ1 / : 51 line res1 res < x b1 : f f1 : 12 mat dnor s1 normi x normi / : cont cont 1 + : Sol cont 1 el cont : z 1 n range Sol cont z 1 + el x z el : 11 line for Sol cont n 2 + el res1 μ1 * : Sol cont n 3 + el μ : Sol cont n 4 + el dnor : μ μ 10 / : update 1 : 101 line μ μ 10 * : update 0 : 21 line if 31 line while 21 line

β x : 0.777335 1.072745 1.278127 4.800822 41 mat

X t : Y y : 12 mat

corr ... SSD

corr Pearson correlation χ X Mean : μ Y Mean : n X rows : 13 mat X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

SSD = "Sum Square Differences" SSD y i el t i el β f - (2^(i 1 n sum :

FIT range, populate U 020 0.01 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 41 line :

tol 0.000004

β 0.777335 1.072745 1.278127 4.800822 41 mat

corr 1.0794

1 time t0 - min 1.5

SSD 0.001

Absolute residuals Δev i 1 t rows range Δ i el y i el t i el β f - 3 round : for t Δ augment 21 line :

Absolute residuals

Δev 0.025 BarSize 1 1 sys

Δev 11012 -^* 0.003 0.51 0.002 0.82 0.023 - 1.02 0.02 1.23 0.003 - 1.43 0.014 - 1.85 0.014 2.05 0.006 - 2.36 0.005 - 4.52 0.005 9.22 0.007 112 mat

Δev FIT SSD corr z Sol res1 res update dnor cont tol μ1 μ h Eps jjh2 jjh1 j i ia t0 m n HEADER BarSize plotG lastError Δev FIT SSD corr Y β z Sol res1 f1 b1 s1 res f update dnor cont tol μ1 μ h Eps x jjh2 jjh1 j Φ ΦΦ i ia t0 m n X y t HEADER BarSize plotG lastError SSD z res1 res update dnor cont tol μ1 μ Eps jjh2 jjh1 j i ia t0 m n

Solution
Sol
1	0.751606093553316	1.06463011926191	1	4	0.3616	0.01	0.062098476611671
2	0.786150008022314	1.07666378188172	1.28358183916576	3.76882691386481	0.068120175270013	0.001	0.075244060193509
3	0.782836595926239	1.06916607191074	1.28106251933515	4.87354999726895	0.014535733388282	0.0001	0.226677285351168
4	0.777152817274993	1.07274809821053	1.27774587931935	4.79296363092467	0.001792014496406	0.00001	0.016813473364234
5	0.777360217058862	1.07274341688277	1.27816740235205	4.80147026881757	0.001492836727217	0.000001	0.001771673553437
6	0.777333304102869	1.07274514283407	1.27812366739621	4.80076309756332	0.001492348944393	0.0000001	0.000147303926455
7	0.77733568299132	1.07274497215174	1.27812729331919	4.80082804903812	0.001492345537878	0.00000001	0.000013529223316
8	0.777335471697208	1.07274498636881	1.27812696248299	4.80082233853284	0.001492345511013	0.000000001	0.000001189484811
#
ITER	S:x.1	S:x.2	S:x.3	S:x.4	Res1	μ	dnor
#
#
#

HEADER ITER β1 β2 β3 β4 Res1 μ dnor 18 mat :

System HEADER Sol stack :

System ITER β1 β2 β3 β4 Res1 μ dnor 1 0.7516 1.0646 14 0.3616 0.01 0.0621 2 0.7862 1.0767 1.2836 3.7688 0.0681 0.001 0.0752 3 0.7828 1.0692 1.2811 4.8735 0.0145 0.0001 0.2267 4 0.7772 1.0727 1.2777 4.793 0.0018 0 0.0168 5 0.7774 1.0727 1.2782 4.8015 0.0015 0 0.0018 6 0.7773 1.0727 1.2781 4.8008 0.0015 0 0.0001 7 0.7773 1.0727 1.2781 4.8008 0.0015 008 0.7773 1.0727 1.2781 4.8008 0.0015 0098 mat

Conjugate Gradient

]]> Minimize Conjugate-Gradient

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

init iter Minimize XY f φ β LS X XY 1 col : Y XY 2 col : n XY rows : k x β φ length 1 - : vx-> raw initial vector fit i 1 X length range vx i el X i el β f eval : for M-> Cholesky GradientMatrix j 1 k range i 1 n range M i j el X i el β φ j 1 + el eval : for for CholeskySolver LeastSquares Φ M transpose M * : d M transpose Y vx - (* : Δβ Φ 1 -^eval d * : b β Δβ + : 131 line : β 1 el init : i 1 : i iter ≤ β i 1 + el XY f φ β i el LS : i i 1 + : 21 line while β β iter el : 41 line β 31 line :

Vector Gradient ... Optimiz Symbolic
seemingly a scalar kernel  not 
recognized in program loop x β f n φ ct 1 : i 1 n range PD ct el x β f (β ct el diff : stack f(x,β) & PD V 1 el x β f : V i 1 + el PD i el : 21 line ct ct 1 + : 41 line for V 31 line :

Error stem plot for QuickPlot unicolor data Error stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

L H N xd U 0 : dx H L - N / : i 1 N 1 + range U i el L dx - (dx i * + : for U 41 line :

Bar plot unicolor style, bar width user. data dt BarSize v data 2 col : t v bar t dt - 0 t dt - v t dt + v t dt + 042 mat : j 1 data rows range j 1 ≡ B data j 1 el data j 2 el bar : B B data j 1 el data j 2 el bar stack : if 11 line for B 41 line :

corr Pearson correlation χ X Mean : μ Y Mean : n XY rows : 13 mat X i el χ - (Y i el μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum Y i el μ - (2^(i 1 n sum * sqrt / X i el χ - (X i el β f eval μ - (* (i 1 n sum X i el χ - (2^(i 1 n sum X i el β f eval μ - (2^(i 1 n sum * sqrt / / 31 line :

correlation between [X,Y data]

correlation ... [X,fitted model]

Absolute  residuals observer
fetches β from calculated δ j 1 XY rows range Δ j el Y j el X j el β f - eval : for X Δ augment 21 line :

SSD = "Sum Square Differences" SSD Y i el X i el β f - (2^(i 1 XY rows sum :

3 appVersion 0.98.6179 ≡ Timing 7 sec ≡ 21 line

clear ln0 undefined ε 1015 -^:

XY ε 0.78 0.51 0.8 0.82 0.92 1.02 1.14 1.23 1.26 1.43 1.28 1.85 1.22 2.05 1.16 2.36 1.12 4.52 1.08 9.22 1.08 112 mat :

x β f β 2 el β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ / + β 1 el β 2 el - 1 x β 3 el / (β 4 el^+ (2^/ x β 3 el / (β 4 el^* β 4 el * - :

Model function

t0 1 time :

in φ(x,β,f,n) -> set 'n' to last index β # el ≡

<= Gradient Vector Function x β φ x β f 4 φ :

X XY 1 col : Y XY 2 col : 12 mat data XY . 12 black plot : n XY rows : 31 line

init 0.5 11114 mat transpose :

iter 9 :

algo solving for β β init iter Minimize :

assign/isolate .. β β :

1 time t0 - s 7

SSD 0.001

Absolute  residuals δ Δ 0 : j 1 XY rows range Δ j el Y j el X j el β f - 3 round eval : for X Δ augment 31 line :

corr 1.0794

.... L-M
identical CG 
wrt Residuals 0.777335509074769 1.07274497889379 1.27812699550013 4.80082359179995 41 mat

bar δ 0.0375 BarSize (:

FIT U 010 0.025 range : i 1 U rows range vy i el U i el β f eval : for U vy augment 31 line :

bar

β 0.77735 1.07274 1.27815 4.80111 41 mat

data XY o 5 black plot :

Title 21 Pharmacokinetics 12 black 15 mat :

collect 1.08 FIT 0.78 data Title 51 sys :

collect